A crucially important conflict, woefully under-reported in the west, has now come to a head in the Middle East. In response to an ongoing fight that could spill out beyond the Arabian peninsula, Saudi Arabia has entered into direct war with the Houthi rebels in northern Yemen.

Saudi military intervention marks the first time in the kingdom's history that its army has crossed its borders without an ally. Previously, the kingdom engaged only in proxy wars. The Saudis used royalist Yemenis to fight Nasser's Egypt in the 1960s, Iraq's Saddam Hussein to fight Iran in the 1980s, and the US to fight Iraq in the 1990s.

Indeed, Saudi Arabia has fought every "ism" that has sought to dominate the Middle East, including Nasser's pan-Arabism, communism, and today's Islamism of the Muslim Brotherhood and Hamas, the terrorism of al-Qaida and the Shi'ism of Iran. The tools it relied upon were oil money and Wahhabi Islam. During the 1980s, Saudi Arabia spent more than $75bn on the propagation of Wahhabi doctrine, funding schools, mosques, and charities across the Islamic world in an effort to bolster its influence.

A large share of these resources was reserved for its back garden, Yemen. Thousands of schools were established, covering every city and village in Yemen. Saudi Arabia created in Yemen a strong Wahhabi current that was politically and ideologically loyal to the ruling al-Saud. Indeed, Yemen's president, Ali Abdullah Saleh, used imported Wahhabism to defeat his domestic opponents – first the communists, then the Houthis – despite being a Zaidi Shia.

But now this policy has backfired, with the Houthis openly rebelling against Wahhabi encroachment on their religious ideology, while themselves encroaching on neighbouring Saudi territory as they fight the government.

After four months of fighting, Saleh's domestic forces had failed to contain the revolt. So, unable to prosecute the war on his own, Saleh turned a domestic rebellion into a sectarian and security threat to the entire Arabian peninsula, thereby manoeuvring the Saudis – eager from the outset to help Saleh, whom they view as their proxy – into providing military backing.

The Saudis' justification for intervening is that their national territory is under threat. But that argument is weak, and there is no national support for this war in either country. Rather, Saudi military intervention reflects the kingdom's wariness toward a hostile Shia region on its southern border, especially given that the same tribes and sects that populate northern Yemen dominate the southern Saudi regions of Jizan and Najran. The Saudi state doubts the loyalty of its own Ismaili and Zaidi populations, whose natural sympathies are suspected to lie with the Houthis.

Southern Saudi Arabia and northern Yemen have thus become a microcosm of the broader civil war playing out in the Muslim world. But Saudi Arabia's intervention in the conflict has also turned what had been a cold war – a war of position and influence within the region – into a hot war with international repercussions.

The principal conflict is between the Saudis and Iran, which has established powerful political bridgeheads in Syria, Lebanon, Iraq, and Gaza. Saleh played a key role in reinforcing Saudi perceptions of a dangerous Iranian security threat, thereby helping to turn the Houthi rebellion into a geopolitical conflict.

Both the Saudi and Yemeni governments have also claimed that there are strong links between the Houthis and al-Qaida, thereby gaining American support. But the Houthis are not terrorists. Abdul Malik al-Houthi, a leader of the insurgency in Yemen's Sa'dah region, said this month that the Houthis, who are Zaidi Shia, are ideologically and strategically antithetical to Wahhabi Sunni al-Qaida.

At the same time, al-Qaida has benefited from the conflict, as the chaos on the rugged and mountainous 1,500km border allows it to smuggle arms and fighters into Saudi Arabia in an attempt to destabilise the kingdom. Sunni areas of Yemen – a weak state, if not a failed one – have become a safe haven for al-Qaida.

But the Saudis are unlikely to succeed militarily in Yemen. Yemen's army of 700,000 could not suppress the Houthi rebellion, despite five attempts since 2004. Now they are leaving Saudi Arabia's untested army of 200,000 men to do the job for them. And, while the Saudis are currently relying on their air force, a full-scale land battle will have to follow – on the same harsh terrain that helped defeated Nasser's battle-hardened troops in the 1960s.

The Houthis, for their part, lack aircraft and armoured vehicles, but have tactical advantages owing to their numbers, experience of the terrain, and skilful use of land mines. They also benefit from disciplined training, reminiscent of Hezbollah's activities in Lebanon.

Saleh has declared that there is no end to this war, but a peaceful solution at this stage would put the Houthis in a stronger position to win their demands, which primarily concern the preservation of culture and identity. For example, the Houthis want a Zaidi university.

Is there a way out? Qatar acted as a mediator last year, and persuaded the Yemeni government to accept a ceasefire. Syria, which enjoys good relations with Yemen, has also offered to mediate. Each of these offers was unacceptable to the Saudi rulers, who fear that submitting the conflict to outside mediation would diminish the kingdom's regional power. For this reason, Iran's offer to mediate was seen as the ultimate provocation.

So the war continues, with no immediate possibility of a peaceful solution – and with the policy failure of Saudi Arabia's military intervention eroding its position in the Arab world. The dilemma for the Saudis is that now the damage will be much greater if they do not crush the Houthis, as this would embolden al-Qaida. This is the biggest threat facing Saudi Arabia, but its rulers' ill-considered war strategy has only brought that threat closer.